National Party MPs are considering whether to support moves to make Monday a public holiday when either Waitangi Day or Anzac Day fall on a weekend.
The Government has raised concerns about the economic cost of any change, while some National MPs have also argued it would devalue both days.
Prime Minister John Key says National MPs will discuss the matter on Tuesday to gauge support or opposition to a bill put forward by Labour Party MP David Clark.
The bill would ensure that if either Waitangi Day and Anzac Day fell on a weekend the following Monday would be a public holiday. It is due to be debated in about six weeks.
The Prime Minister has said the Department of Labour has recommended that the bill not be supported.
John Key says he understands people would prefer to have the day off, but it has to be factored against what it would cost businesses and the economy overall and he wants to look at the data more closely.
The department has suggested the proposed change could cost $200 million, but Labour leader David Shearer dismisses the estimate.
"We looked at the $200 million cost and, if you average it out over the number of years that will be affected and divide by the population, we're actually looking at a few cents per person in New Zealand - and I just think that's a bit mean, actually."
Before National's caucus meeting, Transport Minister Gerry Brownlee expressed reservations about the proposal.
"Those two days are memorial days; the idea is that we remember things that occurred on those days. So it seems to me that you'd cheapen that remembrance by just tacking them on to any old weekend."
But David Shearer says making Monday a public holiday when Waitangi and Anzac Days fell on a weekend would not detract from their importance.
Even without the National Party's support, the bill could still become law if other parties vote for it.